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Answer :
Final answer:
The correct answer is B,The equation whose roots are diminished by 2 from x⁴−5x³+7x²−17x+11=0 is B. x⁴+3x³+x²−17x−19=0.
Explanation:
To find the equation whose roots are diminished by 2 from the roots of x⁴−5x³+7x²−17x+11=0, we need to subtract 2 from each root. Let's call the new roots a and b. The equation will be in the form (x-a)(x-b)=0. Substituting the reduced roots, the equation becomes (x-(a+2))(x-(b+2))=0. Multiplying this out, we get x² - (a+b+4)x + (ab+2a+2b+4)=0. Therefore, the correct equation is B. x⁴+3x³+x²−17x−19=0.
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